Performance of compressible flow codes at low Mach numbers

Abstract

The accuracy and the performance of three two-dimensional compressible flow codes at freestream Mach numbers as low as 0.001 are examined. Two of the codes employ a finite volume discretization scheme along with a multistage time-stepping algorithm to solve the Euler equations. The two codes differ in their respective use of cell-centered and node-centered differencing schemes. The third code uses an implicit finite difference procedure to solve the unsteady Navier-Stokes equations. Computational test cases are the inviscid steady flow over a circular cylinder and the impulsively started viscous flow over a cylinder. Errors in the numerical results are presented as functions of mesh size and computational Mach number. It is shown that for certain classes of problems, the compressible codes can be sufficiently accurate to predict flow features at essentially incompressible speeds and that they can be adequately efficient since there is no need to lower excessively the computational Mach number in order to extract these results.

Simulation of all-scale atmospheric dynamics on unstructured meshes

“…Interestingly, it depends on the solution of a linear elliptic Helmholtz problem for a density perturbation, that in the incompressible limit becomes effectively a Poisson problem for pressure reminiscent of the projection approaches [50,19]. Over the years many ingenious methods have been devised to extend concepts underlying compressible flow solvers to low-Mach number regime [87,61,49,161,34,166,174,116] and/or generalise incompressible concepts to compressible flows [57,60,191,185,11,186,99,181,182]. In computational meteorology the progress of unified models was motivated by the specificity of atmospheric dynamics and goals of weather and climate prediction.…”

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